If I have the two equations y=ax and x=u-y where y is the output and u is the input, how can I get Mathematica to combine these two equations to get the single equation, y = (a/(1+a))u? Thanks.

Ok. That worked. Thanks.

There is a hidden cache of previous assignments that some users don't know about. Had you previously assigned any values or functions to any of those names? Try restarting Mathematica fresh, make certain you don't have any prior assignments and then do only Solve[Eliminate[{y==a x,x==u-y},x],y] and see what you get

Wait. That didn't work for me. I got, In[31]:= Solve[Eliminate[{y == a x, x == u - y}, x], y] During evaluation of In[31]:= $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of u-y. Out[31]= Hold[Solve[Eliminate[{y == a x, x == u - y}, x], y]]

Combine equations to get single feedback equation